本研究討論了自發性光學圖案形成中的碎形維度。我們分析了一個光調製不穩定性現象(Optical Modulation Instability, MI)的實驗結果，並計算出其碎形維度。
　　我們發現MI產生的光學圖案在低光強度閥值(Threshold)下有自我相似(Self-similarity)結構，可以被視為碎形。
　　我們計算出點狀MI圖案的盒子維度(Box-counting Dimension)隨著施加在非線性晶體的電壓增加而逐漸下降，不同雷射光強度的下降趨勢一致。另外我們也發現點狀MI圖案的盒子維度隨著時間作小幅度的上下震盪。

This research discussed the fractal dimension in spontaneous optical pattern formations. We calculated the fractal dimension of the optical patterns generated by optical modulation instability (MI).
By calculating the fractal dimension, we found that at low intensity threshold, MI patterns can be regard as fractals due to its self-similar structure.
We also found that as the voltage applied to the nonlinear crystal increases, the fractal dimension decreases. The decreasing rate is equal among different laser beam intensity.
Finally, we found that the fractal dimension of the MI pattern fluctuated over time.

第1章 序論
第2章 文獻回顧
2-1 光調製不穩定性
2-2 光調製不穩定性實驗
2-3 碎形幾何
2-4 碎形維度
第3章 研究方法
3-1 圖形預處理
3-2 盒子維度演算法
第4章 計算結果與分析
4-1 碎形維度隨選取閥值改變關係
4-2 碎形維度隨電壓改變關係
4-3 碎形維度隨時間改變關係
第5章 總結
參考資料
附錄

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